Elliptic partial differential-algebraic multiphysics models in electrical network design. (English) Zbl 1046.94519
Summary: In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multiphysics approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that combines the differential-algebraic network equations of the circuit with elliptic boundary value problems modeling the diodes. A first existence result is given for this mixed initial-boundary value problem of partial differential-algebraic equations.
MSC:
94C99 | Circuits, networks |
35J25 | Boundary value problems for second-order elliptic equations |
82D37 | Statistical mechanics of semiconductors |
Keywords:
RLC networks; modified network analysis; semiconductors; drift-diffusion equations; coupled systems; partial differential-algebraic equationsReferences:
[1] | Gear, C. W., IEEE Trans. Circuit Theory18, 89 (1971), DOI: 10.1109/TCT.1971.1083221. |
[2] | Günther, M., Partielle Differential-Algebraische Systeme in der Numerischen Zeitbe-reichsanalyse Elektrischer Schaltungen, 2001, VDI |
[3] | Günther, M., Math. Comput. Model. Dynam. Systems7, 189 (2001). · Zbl 1045.93005 |
[4] | Ho, C. W.Ruehli, A. E.Brennan, P. A., IEEE Trans. Circuits Systems22, 505 (1975). |
[5] | Jerome, J. W., Analysis of Charge Transport. A Mathematical Study of Semiconductor Devices, 1995, Springer · Zbl 0835.65151 |
[6] | Hairer, E.; Wanner, G., Solving Ordinary Differential Equation: II, Stiff and Differential-Algebraic Problems, 2002, Springer |
[7] | Markowich, P. A., The Stationary Semiconductor Device Equations, 1986, Springer |
[8] | Markowich, P. A.; Ringhofer, C. A.; Schmeiser, C., Semiconductor Equations, 1990, Springer · Zbl 0765.35001 |
[9] | McCalla, W. J., Fundamentals of Computer Aided Circuit Simulation, 1988, Kluwer |
[10] | Selberherr, S., Analysis and Simulation of Semiconductor Devices, 1984, Springer |
[11] | Taylor, M. E., Partial Differential Equations III — Nonlinear Equations, 1996, Springer · Zbl 0869.35004 |
[12] | Tischendorf, C., Surv. Math. Ind.8, 187 (1999). · Zbl 1085.94513 |
[13] | Zeidler, E., Nonlinear Functional Analysis and its Applications I: Fixed-Point Theorems, 1986, Springer · Zbl 0583.47050 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.